Investing in sports teams and stadiums is usually a bad deal for cities. Glendale, Ariz.'s multimillion-dollar bet on its hockey team looks like one for the penalty box.

Last year, Glendale, Ariz., faced a $35 million budget shortfall. The city responded by laying off 49 employees, cutting social services and raising the city sales tax and some property taxes. A new library and courthouse were delayed until 2017.

Yet Glendale seems to be able to find tens of millions of dollars to try and keep the Phoenix Coyotes playing in the city's Jobing.com Arena. The troubled National Hockey League franchise declared bankruptcy in 2009 and has since been run by the league. Between 2010 and 2012 alone, Glendale paid the NHL $25 million a year to manage the team.

This month, Glendale approved a 15-year, $225 million lease on the arena with Renaissance Sports and Entertainment, a company that plans to buy the Coyotes. A number of deals to buy the team have fallen through since 2009, and this one was dependent on reaching a lease agreement. The deal allows Renaissance to move the franchise after five years if accrued losses top $50 million.

Professional sports teams and facilities are generally an even worse deal for state and local governments than convention centers, and Glendale's story is an all-too-familiar one. All 32 National Football League teams, for example, are on Forbes magazine's list of the 50 most valuable sports franchises, yet only three NFL stadiums were built without public funding.

One problem is that teams' economic impact is often felt only within a few blocks of the stadiums or arenas where they play. An even more fundamental problem is that the overwhelming majority of fans who attend the games live within a short distance of the arena. Rather than representing new economic activity, money generated by sporting events would likely have been spent elsewhere in the local economy, such as at a movie theater.

Sports stadiums "typically aren't a good tool for economic development," said Victor Matheson, an economist at Holy Cross who has studied the economic impact of stadium construction for decades. Interviewed in The Atlantic, Matheson described a simple rule for determining the actual return on investment from sports stadiums: "Take whatever number the sports promoter says, take it and move the decimal one place to the left. Divide it by ten, and that's a pretty good estimate of the actual economic impact."

An Arizona Republic analysis found that even if the Coyotes went to the Stanley Cup Finals for the next 20 seasons and Jobing.com Arena booked 30 sold-out concerts each year for the next 20 years, Glendale could still expect to lose about $9 million annually.

The $25 million a year paid to the NHL to manage the Coyotes is only the beginning of Glendale's costs. For the next 20 years, the city owes $12.6 million per year in debt service for construction of the arena. It also will pay $15 million annually to another firm to manage it, even though the city only budgeted $6 million for arena management. And its lease revenue could disappear after five years if the Coyotes continue to lose money.

Compounding Glendale's problems is the fact that any NHL franchise in the Arizona desert faces dubious prospects. During the 2013 season, the Coyotes were 29th out of 30 NHL teams in attendance. As Matheson -- surely among the most quotable of economists -- put it, "This is hockey in a non-hockey city where the average resident hasn't seen ice outside of a margarita."

You might say that Glendale, like so many other state and local governments that have invested heavily in sports stadiums and franchises, has forgotten the old adage that when you find yourself in a hole, it's probably a good idea to stop digging. Then again, at least the city had the presence of mind to reject one option that was under consideration: offering public buildings such as City Hall and the police station as collateral on the loan it took out to cover its payments to the NHL.